{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "import pandas as pd "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "X = np.linspace(-100,100,400) \n",
    "y = [1/(1+math.e**(-x)) for x in X]\n",
    "plt.plot(X,y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "def loadDataSet():\t\n",
    "    dataMat=[]\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \n",
    "    labelMat=[]\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \n",
    "    fr=open('testSet.txt')  \t\t\t\t\t\t\t\t\t\t\t \n",
    "    for line in fr.readlines():  \t\t\t\t\t\t\t\t\t\t \n",
    "        lineArr=line.strip().split()   \t\t\t\t\t\t\t\t\t \n",
    "        dataMat.append([1.0,float(lineArr[0]),float(lineArr[1])]) \t     \n",
    "        labelMat.append(int(lineArr[2]))   \t\t\t\t\t\t\t\t\n",
    "    fr.close() \t\t\t\t\t\t\t\t\t\t\t\t\t\t\t \n",
    "    return dataMat,labelMat \t\t\t\t\t\t\t\t\t\t\t \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plotDataSet():\n",
    "    dataMat, labelMat = loadDataSet()                                   \n",
    "    dataArr = np.array(dataMat)                                         \n",
    "    n = np.shape(dataMat)[0]                                            \n",
    "    xcord1 = []; ycord1 = []                                           \n",
    "    xcord2 = []; ycord2 = []                                          \n",
    "    for i in range(n):                                           \n",
    "        if int(labelMat[i]) == 1:\n",
    "            xcord1.append(dataArr[i,1]); ycord1.append(dataArr[i,2])   \n",
    "        else:\n",
    "            xcord2.append(dataArr[i,1]); ycord2.append(dataArr[i,2])   \n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)                                          \n",
    "    ax.scatter(xcord1, ycord1, s = 20, c = 'red', marker = 's',alpha=.5)\n",
    "    ax.scatter(xcord2, ycord2, s = 20, c = 'green',alpha=.5)            \n",
    "    plt.title('DataSet')                                               \n",
    "    plt.xlabel('x'); plt.ylabel('y')                                   \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [],
   "source": [
    "def sigmoid(inX):\n",
    "    return 1.0/(1+np.exp(-inX))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gradAscent(dataMatIn,classLabels):\t\t\t\t\t\n",
    "    dataMatrix=np.mat(dataMatIn)      \t\t\t\t\t\t\t\n",
    "    labelMat=np.mat(classLabels).transpose()  \t\t\t\t     \n",
    "    m,n=np.shape(dataMatrix)       \t\t\t\t\t\t\t\t \n",
    "    alpha=0.001   \t\t\t\t\t\t\t\t\t\t\t     \n",
    "    maxCycles=500\t\n",
    "    weights=np.ones((n,1))\n",
    "    for k in range(maxCycles):\n",
    "        h=sigmoid(dataMatrix*weights)   \t\t\t\t\t\t \n",
    "        error=labelMat-h   \n",
    "        weights=weights+alpha*dataMatrix.transpose()*error       \n",
    "    return weights.getA() \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def stocGradAscent0(dataMatrix,classLabels):    \n",
    "    \n",
    "    m,n=np.shape(dataMatrix)\n",
    "    alpha=0.01\n",
    "    weights=np.ones(n)\n",
    "    for i in range(m):\n",
    "        h=sigmoid(sum(dataMatrix[i]*weights))\n",
    "        error=classLabels[i]-h\n",
    "        weights=weights+alpha*error*dataMatrix[i]\n",
    "    return weights\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "def plotBestFit(weights):\t\t\n",
    "    dataMat, labelMat = loadDataSet()                                   \n",
    "    dataArr = np.array(dataMat)                                        \n",
    "    n = np.shape(dataMat)[0]                                            \n",
    "    xcord1 = []; ycord1 = []                                            \n",
    "    xcord2 = []; ycord2 = []                                            \n",
    "    for i in range(n):                                                 \n",
    "        if int(labelMat[i]) == 1:\n",
    "            xcord1.append(dataArr[i,1]); ycord1.append(dataArr[i,2])    \n",
    "        else:\n",
    "            xcord2.append(dataArr[i,1]); ycord2.append(dataArr[i,2])    \n",
    "    fig = plt.figure()\n",
    "    ax = fig.add_subplot(111)                                           \n",
    "    ax.scatter(xcord1, ycord1, s = 20, c = 'red', marker = 's',alpha=.5)\n",
    "    ax.scatter(xcord2, ycord2, s = 20, c = 'green',alpha=.5)            \n",
    "    x = np.arange(-3.0, 3.0, 0.1)\n",
    "    y = (-weights[0] - weights[1] * x) / weights[2]                     \n",
    "\t\n",
    "    ax.plot(x, y)\n",
    "    plt.title('BestFit')                                                \n",
    "    plt.xlabel('X1'); plt.ylabel('X2')                                 \n",
    "    plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[[ 4.12414349]\n",
      " [ 0.48007329]\n",
      " [-0.6168482 ]]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[ 1.01702007  0.85914348 -0.36579921]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[14.07395702  0.87486585 -2.0881661 ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def main():\n",
    "    dataArr, labelMat = loadDataSet()\n",
    "    \n",
    "    plotDataSet()\n",
    "    weights1 = gradAscent(dataArr, labelMat)     \n",
    "    print(weights1)\n",
    "    plotBestFit(weights1)\n",
    "\n",
    "    dataArr, labelMat = loadDataSet()\n",
    "    weights2 = stocGradAscent0(np.array(dataArr), labelMat)      \n",
    "    print(weights2)\n",
    "    plotBestFit(weights2)\n",
    "\n",
    "    dataArr, labelMat = loadDataSet()\n",
    "    weight3 = stocGradAscent1(np.array(dataArr), labelMat)   \n",
    "    print(weight3)\n",
    "    plotBestFit(weight3)\n",
    "\n",
    "\n",
    "if __name__ == '__main__':\n",
    "    main()\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.10.6"
  },
  "orig_nbformat": 4
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
